Let $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ 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 $a x^2+b x+c=0$ has all real roots is $$\frac{m}{n}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$$, then $\mathrm{m}+\mathrm{n}$ is equal to $\underline{\hspace{2cm}}$.