#### Answer

$(-1, 0) \cup (1, +\infty)$

#### Work Step by Step

Graph
$y_1 =x^{1/3}$ (the orange graph) and
$y_2=x$ (the purple graph)
on the same coordinate plane.
(refer to the attached image below for the graph)
The solution to the given inequality is the set of x-values for which $y_1 \lt y_2$.
Notice that $y_1$ (the orange graph) is less than $y_2$ in the following intervals:
$(-1, 0)$ and $(1, +\infty)$
Thus, the solution to the given inequality is:
$(-1, 0) \cup (1, +\infty)$