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f(x)=(sin−1x)3+(cos−1x)3\large f(x) = {\left(\sin^{-1}x\right)}^3 + {\left(\cos^{-1}x\right)}^3f(x)=(sin−1x)3+(cos−1x)3
For real xxx, if the sum of the minimum and maximum values of the function above can be represented as abπ3\dfrac{a}{b} \pi^3baπ3, where aaa and bbb are coprime positive integers, then what is the value of a+ba+ba+b?
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