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…

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