2017 Fermat Problem 19

A point is *equidistant from the coordinate axes* if the vertical distance from the point to the x-axis is equal to the horizontal distance from the point to the y-axis. The point of intersection of the vertical line x = a with the line with equation 3x + 8y = 24 is equidistant from the coordinate axes. What is the sum of all possible values of a?

\textbf{(A)}\ 0\quad \textbf{(B)}\ -\frac{144}{55}\quad \textbf{(C)}\ -\frac{11}{5}\quad \textbf{(D)}\ \frac{24}{11}\quad \textbf{(E)}\ 8

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.