Answer
$$x∈(-\infty, 1]∪[2,3]$$
Also see the image below.
Work Step by Step
$x^3+11x≤6x^2+6$
$x^3+11x$ is represented as the Blue graph on the image above.
$6x^2+6$ is represented as the Red graph on the image above.
There are $3$ intersection points($A$, $B$, and $C$ on the image). With these intersections we have $4$ regions. Our solution is in the regions where the Blue graph lies below the Red one. Those are the regions:
$(-\infty, 1]∪[2,3]$
