Fracture of the problem

Calculus Level pending

\[{ \left( \sum _{ x=0 }^{ \infty }{ \frac { \left( 2x \right) !\left( { x }^{ 2 }+5x+16 \right) \left( { 5 }^{ x }+{ 6 }^{ x } \right) }{ { 30 }^{ x }{ \left( x! \right) }^{ 2 } } } \right) }^{ 2 } \]

If the value of the expression above is in the form of \(125\left( a+16\sqrt { b } \right) \), where \(a\) and \(b\) are positive integers, find \(a+b\).

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