String otimizing challenge

This challenge will work with Strings composed by groups of pairs of numbers. All pairs are separated by slashes and all numbers in each pair are separated by a comma. This is a example of input: -2,3/5,-4/6,0/-3,0/-5,-5/0,-3/-4,0/0,-3/.

The main aim is otimize the sequence by removing the excess of 0,0 pairs. When a 0,0 is removed from the middle of the sequence the surrounding pairs should be merged into a new single one.

Look to this format:
a,b/0,0/c,d

To merge pairs after remove 0,0 the new pair should be:
a+c,b+d.

Obs.: The input may contains more than one 0,0 pair, in addition, it can contains severals 0,0 in a row as well.

Obs.: 0,0 can appears at begin or end of the sequence. In these cases it just need to be removed (all leading slashes are turned to only 1 -> "/0,0/1,0/" -> "/1,0/").

Example:

Input: "3,2/0,0/-2,1/";
Removing 0,0: "3,2//-2,1/";
Merging previous and next groups: (3+(-2),2+1): "1,3/"

------------------------------------------
Another example:

Input: "6,-1/3,1/3,3/0,0/-3,-3/-3,-1/6,1"
Removing 0,0: "6,-1/3,1/3,3//-3,-3/-3,-1/6,1"
Merging previous and next groups (3+(-3),3+(-3)):  "6,-1/3,1/0,0/-3,-1/6,1"*

*Removing 0,0: "6,-1/3,1//-3,-1/6,1"
Merging previous and next groups (3+(-3), 1+(-1)): "6,-1/0,0/6,1"*

*Removing 0,0: "6,-1//6,1"
Merging previous and next groups (6+(6), -1+(1)): "12,0"*

--------------------------------------------
*FORMATTING RULES (Optional challenge)

The max value for numbers should be 6. This means that, if you get a sum case
wich result is > 6, you need replace it to 12 - (result).
Example:
6 + 6 = 12 (result 12, wrong);
6 + 6 = 12 - (12) = 0 (this means a 12 value takes same effect a 0 value).
Other example:
5 + 4 = 9 (result 9, wrong)
5 + 4 = 12 - 9 = 3 (should be -3, look observation bellow)*.

*Obs.: If the result is > 0 (positive) the final value should be negative and if the result is negative, the final result should be 12 + result, intead 12 - result. Example:
-5 + -4 = -9 (wrong and operation with 12 should be +, instead - )
-5 + -4 = 12 + (-9) = 3.