# Summing the sum

Calculus Level 5

$\large \sum _{ a=1 }^{ \infty }{ \sum _{ b=1 }^{ \infty }{ \dfrac { 1 }{ { a }^{ 2 }{ ( a+b ) }^{ 4 } } } } =-\dfrac { A }{ B } \zeta \left( C \right) +( { \zeta }( D ))^E$

The equation above holds true for positive integers $$A,B,C,D$$ and $$E$$, where $$A$$ and $$B$$ are coprime. Find $$A+B+C+D+E$$.

Notation: $$\zeta(\cdot)$$ denotes the Riemann zeta function.

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