AMC 12 2005b Problem 24

All three vertices of an equilateral triangle are on the parabola $y=x^2$, and one of its sides has a slope of $2$. The $x$-coordinates of the three vertices have a sum of $m/n$, where $m$ and $n$ are relatively prime positive integers. What is the value of $m+n$?

\textbf{(A)}\ 14 \textbf{(B)}\ 15 \textbf{(C)}\ 16 \textbf{(D)}\ 17 \textbf{(E)}\ 18