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 ________.
