Matrices and Determinants: JEE Main 2026 Mathematics question

Let $n$ be the number obtained on rolling a fair die. If the probability that the system $x-ny+z=6$, $x+(n-2)y+(n+1)z=8$, $(n-1)y+z=1$ has a unique solution is $\frac{k}{6}$, then the sum of $k$ and all possible values of $n$ is :