The function $f$ is defined by $f(x)=(x-r_1)(x-r_2)(x-r_3)$, where $r_1,r_2,$ and $r_3$ are distinct real numbers. If $f(2m+1)=0$, where $m$ is a constant, let $S$ be the sum of the distinct real roots of $f(x)$, and let $T$ be the sum of all possible values of $m$. Which of the following expresses $T$ in terms of $S$?