Answer
$f(x)=\sqrt[3]{x-1}$
Work Step by Step
Given the standard function, $
f(x)=\sqrt[3]{x}
$, the equation of the graph that shifts to the right will have a negative constant added to the $x-$variable. Hence, a shift of $1$ unit to the right will have the equation,
\begin{array}{l}\require{cancel}
f(x)=\sqrt[3]{x-1}
.\end{array}