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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