Domain of y=∛-3x+5

I don't seem really to grasp the concept of prime roots.

It said on symbolab that the domain is (-∞,∞), but how?

Since you can take the cube root of any number (even a negative), no number is not included in the domain. The domain is all really numbers. the whole negative infinity to infinity is saying that in a different way. It says, the domain goes from negative infinity to infinity, so theres is no number that would not work.