The process for "rationalizing" the square-root denominators was to create a situation in which you doubled (by multiplying by another copy of) whatever factors remained inside the radical, since square roots required squares in order to simplify.
The process for cube-root denominators has the same philosophy. But cube roots to not require squares
in order to simplify. What do they need instead? So do you need to double
the factors, or do something else?
For an explanation and examples, try this page