Probability

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 _________.