Calculating pressure inside a solid sphere

A uniform solid sphere has mass MM and radius RR. The pressure PP inside the sphere caused by gravitational compression as a function of distance rr from the center of the sphere is given by P(r)=abGM2πR4(1r2R2), P(r) = \dfrac ab \cdot \dfrac{GM^2}{\pi R^4} \left( 1 - \dfrac{r^2}{R^2} \right), where aa and bb are coprime positive integers.

Find the value of a+ba+b.

Notation: GG denotes the universal gravitational constant: G=6.67×1011 Nm2/kg2G = \SI[per-mode=symbol]{6.67e-11}{\newton\meter\squared\per\kilogram\squared}.

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