We found 78 triples for 7 ≦ rad(a) < 8, 285 ≦ rad(b) < 286! Here you go:

69255 + 232630513917952 = 232630513987207,

q=1.022229365227669

3384375 + 4747558125568 = 4747561509943,

q=1.1673803782583678

15582375 + 558545864067701632 = 558545864083284030,

q=1.0042120974627549

282475249 + 986665376 = 1269140625,

q=1.0000317112696158

1736184375 + 79792264561427626 = 79792266297612000,

q=1.0039710761263534

2401 + 18326388224 = 18326390625,

q=1.0479957585351294

18326390625 + 79792247971221376 = 79792266297612000,

q=1.0106636583544215

30376281825 + 79792235921330176 = 79792266297612000,

q=1.0006741758980406

2401 + 170393268224 = 170393270625,

q=1.0010148834266364

282475249 + 171051509126 = 171333984375,

q=1.0361677259982134

117649 + 192383000576 = 192383118225,

q=1.0284747030881267

7 + 362018054288 = 362018054295,

q=1.013229692029981

74859649024 + 603363423825 = 678223072849,

q=1.0597893553731736

1314762890625 + 31918167678976 = 33232930569601,

q=1.0250119176902321

1314762890625 + 1627098835019824 = 1628413597910449,

q=1.0030316687109098

2401 + 1484437638224 = 1484437640625,

q=1.0052896832836624

1484437640625 + 1626929160269824 = 1628413597910449,

q=1.0007752068095428

1676009510625 + 79790590288101376 = 79792266297612000,

q=1.0572001633931027

49 + 8326831640576 = 8326831640625,

q=1.0008820954749043

9393310546875 + 558536470772737132 = 558545864083284030,

q=1.042306619554598

2401 + 9401438388224 = 9401438390625,

q=1.0496326527381765

40353607 + 12370273318268 = 12370313671875,

q=1.0270872844399157

16807 + 13878052717568 = 13878052734375,

q=1.062326234160601

11797651038976 + 21435279530625 = 33232930569601,

q=1.0225689922294068

335417353126 + 32897513216475 = 33232930569601,

q=1.0431533869711789

2401 + 34391715155624 = 34391715158025,

q=1.0018927531990547

117649 + 64250244022976 = 64250244140625,

q=1.021301402062438

13841287201 + 64236402853424 = 64250244140625,

q=1.0033221851768888

678223072849 + 63572021067776 = 64250244140625,

q=1.0468585511590112

33232930569601 + 39309032321024 = 72541962890625,

q=1.0204286130568094

5764801 + 78277582125824 = 78277587890625,

q=1.019793426827179

2401 + 295821650388224 = 295821650390625,

q=1.0757870102711562

678197021484375 + 10720698163888768 = 11398895185373144,

q=1.0398713902297059

232630513987207 + 593632913747168 = 826263427734375,

q=1.0286259820754577

859792878950625 + 78932473418661376 = 79792266297612000,

q=1.0561330182757038

40353607 + 1529355899691008 = 1529355940044615,

q=1.0210069349756754

96889010407 + 1529259051034208 = 1529355940044615,

q=1.097800792931673

117649 + 3139801025272976 = 3139801025390625,

q=1.002952950824442

13841287201 + 3139787184103424 = 3139801025390625,

q=1.0205748828642616

49 + 4248210944568326 = 4248210944568375,

q=1.030107185348514

4747561509943 + 4243463383058432 = 4248210944568375,

q=1.0557159102834561

11800585957134375 + 546745278126149632 = 558545864083284030,

q=1.0011655414472302

2978037023611232 + 11398895185373143 = 14376932208984376,

q=1.0433072891212778

33232930569601 + 19634410331321024 = 19667643261890624,

q=1.0786930187263022

282475249 + 24114689189477876 = 24114689471953124,

q=1.007705297959644

13841287201 + 27053862159103424 = 27053876000390624,

q=1.0062975015994307

49 + 69643223195000576 = 69643223195000620,

q=1.0557927740422508

282475249 + 71946861121955576 = 71946861404430824,

q=1.1589214316535987

823543 + 74737044394360832 = 74737044395184370,

q=1.0377271642435457

1161341541314176 + 78630924756297825 = 79792266297612000,

q=1.0207285257147245

40353607 + 84382121359904768 = 84382121400258370,

q=1.0006731980169254

678223072849 + 90553291911147776 = 90553970134220620,

q=1.0352970216235087

11764331602778624 + 79792266297612001 = 91556597900390620,

q=1.1298091663238012

1977326743 + 95271927353434112 = 95271929330760850,

q=1.0187451569919623

13841287201 + 98338202468165924 = 98338216309453120,

q=1.0063937936739256

343 + 119911435674051032 = 119911435674051380,

q=1.0255993677315138

823543 + 131051541259672832 = 131051541260496370,

q=1.0177556381001438

5764801 + 135898590082125824 = 135898590087890620,

q=1.0006650605511733

333087321316809375 + 3576733727266178674 = 3909821048582988000,

q=1.0043517270052718

823543 + 552097494355282472 = 552097494356106050,

q=1.04799483906112

335459639924632 + 558210404443359375 = 558545864083284000,

q=1.0303965483424018

147548658832118 + 558545864083284007 = 558693412742116160,

q=1.0159309248092472

11398895185373143 + 565275830086111232 = 576674725271484400,

q=1.0011305843211704

92550751659450368 + 558545864083284007 = 651096615742734300,

q=1.0696340289975623

4747561509943 + 735118163941274432 = 735122911502784300,

q=1.0163835065552294

4747561509943 + 793241616647474432 = 793246364208984300,

q=1.0021117033891929

336297428153044118 + 558545864083284007 = 894843292236328200,

q=1.0027861075652602

33232930569601 + 1265698588073306024 = 1265731821003875800,

q=1.0241177699712012

79792266297612001 + 1530925659727778624 = 1610717926025390600,

q=1.0118959871223971

7 + 3131235648193359368 = 3131235648193359400,

q=1.0013845460403406

343 + 3234809747021484032 = 3234809747021484500,

q=1.0006155675250938

16807 + 3652273260052717568 = 3652273260052734500,

q=1.0171186052019956

112625585571361174 + 3797195463011626875 = 3909821048582988300,

q=1.024040771992414

823543 + 4123611899703160832 = 4123611899703984000,

q=1.0006120790777149

823543 + 4449650657958160832 = 4449650657958984000,

q=1.0492029764357165

4747561509943 + 4449645910397474432 = 4449650657958984000,

q=1.0150827926570085

40353607 + 4655778439477280768 = 4655778439517635000,

q=1.0339774297684077

7 + 4805622710595703118 = 4805622710595703000,

q=1.002374396958549