Fill in the blank to correctly complete the sentence below. If $f(x)=x^{3}$, then $f^{-1}(x)=\square$.

Step 1 ：Start with the function \(f(x) = x^{3}\).

Step 2 ：Rewrite it as \(y = x^{3}\).

Step 3 ：Switch \(x\) and \(y\) to get \(x = y^{3}\).

Step 4 ：Solve for \(y\) by taking the cube root of both sides to get \(y = \sqrt[3]{x}\).

Step 5 ：\(\boxed{f^{-1}(x) = \sqrt[3]{x}}\) is the inverse function.