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Calculus Level 5

\[ \large \displaystyle\sum _{ n=1 }^{ \infty }{ { (-1) }^{ n }\dfrac { \ln { n } }{ { n }^{ 2 } } } =\dfrac { \zeta (a) }{ b } \left( \ln { c\pi } -d\ln { A } +f\gamma \right) \]

The equation above holds true for positive integers \(a,b,c,d\) and \(f\). Find \(a+b+c+d+f\).

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