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 $m+n$? $\mathrm{(A)}\ {{{14}}} \qquad$ $ \mathrm{(B)}\ {{{15}}} \qquad$ $ \mathrm{(C)}\ {{{16}}} \qquad$ $ \mathrm{(D)}\ {{{17}}} \qquad$ $ \mathrm{(E)}\ {{{18}}}$