Let $p(x)$ be a polynomial with integer coefficients. Assume that $p(a) = p(b) = p(c) = -1$, where $a, b, c$ are three different integers. Prove that $p(x)$ has no integral zeros.

Find the value of $(2 + \sqrt{5})^{1/3} - (-2 + \sqrt{5})^{1/3}$.