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Calculus Level 5

$\large \displaystyle\sum _{ n=1 }^{ \infty }{ \displaystyle\sum _{ k=1 }^{ \infty }{ \dfrac { \zeta (n+k)-1 }{ n+k } } } =a\gamma +b$

The equation holds true for integers $$a$$ and $$b$$, with $$\gamma$$ denote the Euler-Mascheroni constant, $$\gamma \approx 0.5772$$.

Find $$a+b$$.

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

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