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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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