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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