Matrices And Determinants

Let n be the number obtained on rolling a fair die. If the probability that the system

$$ \begin{aligned} & x-\mathrm{n} y+z=6 \\ & x+(\mathrm{n}-2) y+(\mathrm{n}+1) z=8 \\ & \quad(\mathrm{n}-1) y+z=1 \end{aligned} $$

has a unique solution is $\frac{k}{6}$, then the sum of $k$ and all possible values of $n$ is :