AHSME 1969 Problem 35

Let $L(m)$ be the $x$ coordinate of the left end point of the intersection of the graphs of $y=x^2-6$ and $y=m$, where $-6<m<6$. Let $r=[L(-m)-L(m)]/m$. Then, as $m$ is made arbitrarily close to zero, the value of $r$ is: $\text{(A) arbitrarily close to } 0 \\ \text{(B) arbitrarily close to }\frac{1}{\sqrt{6}} \text{(C) arbitrarily close to }\frac{2}{\sqrt{6}} \text{(D) arbitrarily large} \text{(E) undetermined}$