Now that's what I call a series! Number 2

Algebra Level 4

m=1m3+(m2+1)2(m2+m)(m4+m2+1) \large \sum_{m=1}^\infty \frac{ m^3 + (m^2+1)^2}{ (m^2+m)(m^4+m^2+1) }

If the series above can be expressed as AB\frac AB for coprime positive integers AA and BB, find the value of A+BA+ B.

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