Answer
See graph (red).
domain $(-\infty,\infty)$, range $(-\infty,\infty)$.
Work Step by Step
Step 1. To obtain the graph of $f(x)=\sqrt[3] {-x}$ from $y=\sqrt[3] x$, reflect the curve across the y-axis. See graph (red).
Step 2. We can find the domain $(-\infty,\infty)$ and the range $(-\infty,\infty)$.