\[\large \sum_{k = 1}^{\infty} \left(\dfrac{1}{3k-1}-\dfrac{1}{3k}\right)\]

The above sum has a closed form of \[\large \dfrac{\ln{A}}{B} - \dfrac{\pi\sqrt{C}}{D^2 E} \; \] where \(A,B,C,D\) and \(E \) are positive prime numbers. Find the value of \(A+B+C+D+E\).

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