# 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 $$a+b$$?

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