Question:

Let $a$, $b$ and $c$ denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1, 2, 3, 4. If the probability that $ax^2+bx+c=0$ has all real roots is $\frac{m}{n}$, $\gcd(m,n)=1$, then $m+n$ is equal to