\[\sum _{ n=1 }^{ \infty }{ \dfrac { { \psi }^{ 1 }\left( n \right) }{ n^2 } } =\frac{A}{B} \zeta \left( C\right)\] If the equation above is true for some positive integers \(A\), \(B\), and \(C\), with \(A,B\) coprime, find \(A+B+C\).

- where\( {\psi}^{1}\) denoted as the polygamma function of the first order
- \(\zeta (x)\) is the Riemann zeta function

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