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