Maximizing and minimizing inverse trigo functions

Geometry Level 5

$\large f(x) = {\left(\sin^{-1}x\right)}^3 + {\left(\cos^{-1}x\right)}^3$

For real $x$ , if the sum of the minimum and maximum values of the function above can be represented as $\dfrac{a}{b} \pi^3$ , where $a$ and $b$ are coprime positive integers, then what is the value of $a+b$ ?