# Minimum and maximum value

Algebra Level 5

$f(a)=\sqrt[3]{a+\frac{a+1}{3}\sqrt{\frac{8a-1}{3}}}+\sqrt[3]{a-\frac{a+1}{3}\sqrt{\frac{8a-1}{3}}}$

For $$a\geq \dfrac18$$, we define $$f(a)$$ as above. Let $$x$$ and $$y$$ be the minimum and maximum values of $$f(a)$$ respectively. Find $$100x-31y$$.

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