Convergence of Triangular number sums. Let us mop it up !

If the sum of reciprocals of cubes of all the triangular numbers converges to the number $A$ ,

$A = 1 + \dfrac{1}{3^3} + \dfrac{1}{6^3} + \dfrac{1}{{10}^3} + \dfrac{1}{{15}^3} + \dfrac{1}{{21}^3} + \dfrac{1}{{28}^3} + \dfrac{1}{{36}^3} + \dfrac{1}{{45}^3} + \cdots$

and the sum of reciprocals of squares of all the triangular numbers converges to the number $B$ ,

$B = 1 + \dfrac{1}{3^2} + \dfrac{1}{6^2} + \dfrac{1}{{10}^2} + \dfrac{1}{{15}^2} + \dfrac{1}{{21}^2} + \dfrac{1}{{28}^2} + \dfrac{1}{{36}^2} + \dfrac{1}{{45}^2} + \cdots$

then $\dfrac AB$ can be expressed as $M \dfrac{\left( P - \pi^2 \right)}{\left( \pi^2 - O \right)}$ where $M, O$ and $P$ are positive integers.

Find $M+O+P$ .