Answer
$x^{1/3}$ or $\sqrt[3]{x}$
Work Step by Step
To find the equation for $f^{-1}$, replace $f(x)$ with $y$, interchange $x$ and $y$, and solve for $y$. This gives $f^{-1}(x)$.
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$ y=x^{3}\qquad$ ... swap x and y
$ x=y^{3}\qquad /(...)^{1/3}\quad$... solve for y
$x^{1/3}=y$
(RHS:$ (y^{3})^{1/3}=y^{3\cdot\frac{1}{3}}=y^{1}=y)$
$y=f^{-1}(x)=x^{1/3}$
