Squiggly Spherical Surface

${ x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \le 225\\{ (x-20) }^{ 2 }+{ (y-15) }^{ 2 }+{ z }^{ 2 }\le 400$

Two balls are represented by the equations above.

Their union is a solid figure with surface area $A\pi$ and volume $B\pi$

Calculate the sum of the coefficients of the monic quadratic with roots $\frac { A }{ 10 }$ and $\sqrt { B }$