Help Please.

How many real numbers are not in the domain of the function$f(x) = \frac{1}{x-64} + \frac{1}{x^2-64} + \frac{1}{x^3-64}$?

EDIT: What I've tried:

-Making an X-Y table

-using DESMOS

-Asking Tutor(who said try an x-y table)

-Asking mom

-Looking it up online

-Sleeping on it

Torquise= not really helpful in my experience