ContourPlot3D[(x^2 + 9/4 y^2 + z^2 - 1)^3 == x^2 z^3 + 9/80 y^2 z^3,
  {x, -6/5, 6/5}, {y, -6/5, 6/5}, {z, -6/5, 3/2},
  Mesh -> None, Boxed -> False, AxesLabel -> {"x", "y", "z"},
  PlotPoints -> 50, Axes -> False,
  ContourStyle -> Directive[Red, Opacity[0.58], Specularity[Yellow, 30]],
  AspectRatio -> 1.15, ViewPoint ->{-0.930, -3.137, -0.860}]

ContourPlot3D[(x^2 + 9/4 y^2 + z^2 - 1) == CubeRoot[x^2 z^3 + 9/80 y^2 z^3],
{x, -6/5, 6/5}, {y, -6/5, 6/5}, {z, -6/5, 3/2}, Mesh -> None, Boxed -> False,
 AxesLabel -> {"x", "y", "z"}, Axes -> False,
 ContourStyle -> Directive[Red, Opacity[0.58], Specularity[Yellow, 30]],
 AspectRatio -> 1.15, ViewPoint -> {-0.930, -3.137, -0.860}]

(x^2 + 9/4 y^2 + z^2 - 1)^3 == x^2 z^3 + 9/80 y^2 z^3 /. z -> 0

(-1 + x^2 + (9 y^2)/4)^3 == 0