Telescopic summation

Algebra Level 3

132+1+142+2+152+3 +162+4 + \large \frac{1}{3^2+1} +\frac{1}{4^2 +2}+ \frac{1}{5^2+3}\ + \frac{1}{6^2+4}\ + \cdots

The series above can be expressed as mn \dfrac mn, where mm and nn are coprime positive integers.

Find m+nm+n.

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