$\large \displaystyle f(x) = (\arcsin(x))^3 + (\arccos(x))^3$

If the sum of the maximum and minimum values of the function $f \colon \mathbb R \to \mathbb R$ can be expressed as $\displaystyle \dfrac{a { \pi}^{b}}{c}$, where $a,b$ and $c$ are positive integers with $a,c$ coprime, find $a+b+c$.