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 $A+ B$ .