AHSME 1975 Problem 12

If $a \neq b, a^3 - b^3 = 19x^3$, and $a-b = x$, which of the following conclusions is correct? $\textbf{(A)}\ a=3x \textbf{(B)}\ a=3x \text{ or } a = -2x \textbf{(C)}\ a=-3x \text{ or } a = 2x \\ \textbf{(D)}\ a=3x \text{ or } a=2x \textbf{(E)}\ a=2x$