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

Algebra Level 4

\[ \large \sum_{m=1}^\infty \frac{ m^3 + (m^2+1)^2}{ (m^2+m)(m^4+m^2+1) } \]

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

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