Once there were cubes and spheres

Geometry Level 4

A sphere and a cube have the same surface area. If the ratio of the volume of the cube to the sphere can be expressed in the form

(AB)n \left(\frac {A}{B}\right)^{n}

where A=πA = \pi, BB is an integer, and nn is rational, find the value of A+B+n A+B+n.

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