2005 AMC 12B 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?

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.