If y = x, then that means where we see y, we can substitute x, because they are equal, so we can re-write the equation y = x3 as x = x3.
What value(s) of x satisfy x = x3? Zero is one value that does, and if x isn't zero, you can divide both sides of this by x to find the other values of x that work. Remember that y = x, so your points of intersection are in the form of (x, x) for all values of x.
Hope this helps,
Stephen La Rocque.