Answer
$(-\infty,-4)\cup(-4,\infty)$
Work Step by Step
The numerator is defined for all real numbers x, as the third root exists for all reals.
The denominator is defined for all x.
We need to exclude the ones that yield 0
$\sqrt[3]{2x}=-2\quad/ (...)^{3}$
$2x=-8$
$x=-4$
Domain of f:
$(-\infty,-4)\cup(-4,\infty)$