Sita and Gita both have a pair of tetrahedral dice who faces are marked as 1,2,3, and 4, The lowest face being regarded as the out come.  They throw their dice simultaneously.  If $P=\frac{a}{b}$  be the probability expressed in lowest term, that the sum of the numbers on their dice is different, find the sum of the digits of value $\left(a+b\right)$