# Warming up summation

Calculus Level 5

$\large \sum _{ n=1 }^{ \infty }{ \sum _{ k=n+1 }^{ \infty }{ \dfrac { { H }_{ n } }{ { k }^{ 6 } } } } =\dfrac { { \pi }^{ A } }{ B } -\dfrac { ({ \zeta }( C ))^2 }{ D } -\zeta ( E )$

The above equation holds true for positive integers $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ with $$C$$ and $$E$$ are odd numbers.

Find $$A+B+C+D+E$$.

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