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$\sum _{ k=1 }^{ \infty }{ \dfrac { { \psi }^{ 1 }\left( k \right) }{ k } } =\sum _{ n=1 }^{ \infty }{ \dfrac { A }{ { n }^{ B } } }$

If the equation above holds true for positive integers $A$ and $B$, find $A+B$.

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