Question 14A triangle has vertices $(0, 0),$ $(1, 1),$ and $(6m, 0),$ and the line $y = mx$ divides the triangle into two triangles of equal area. What is the sum of all possible values of $m?$$-\dfrac{1}{3}$$-\dfrac{1}{6}$$\dfrac{1}{6}$$\dfrac{1}{3}$$\dfrac{1}{2}$