The Astroid

The volume and surface area of the region bounded by the surface ${ x }^{ \frac { 2 }{ 3 } }+{ y }^{ \frac { 2 }{ 3 } }+{ z }^{ \frac { 2 }{ 3 } }=1$ can be expressed by formulas $\frac { 2\left( B-A \right) \pi }{ AB }$ and $\frac { \left( 2A+B \right) \pi }{ A+B }$ , respectively, where $A$ and $B$ are coprime integers.

Find $A+B$ .