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

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 \(\sqrt { B }\)

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