Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations x+y+z=1; 2 x+ Ny +2 z=2; 3 x+3 y+ N…

Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations $$\begin{aligned} & x+y+z=1 \\ & 2 x+\mathrm{Ny}+2 z=2 \\ & 3 x+3 y+\mathrm{N} z=3 \end{aligned} $$ has unique solution is $\displaystyle \frac{k}{6}$, then the sum of value of k and all possible values of N is