A triangle has vertices (0,0),(1,1), and (6 m, 0), and the line y=m x divides the triangle into two triangles of equal area. What is the sum of all possible values of m ?
Answer Choices
A. -\dfrac{1}{3}
B. -\dfrac{1}{6}
C. \dfrac{1}{6}
D. \dfrac{1}{3}
E. \dfrac{1}{2}