March Break 2024 - Problem 1

Let there be $2$ identical unfair $10$-sided die with sides labeled $1-10$. $P$ denotes the probability that the $2$ die roll equal values. If $\min(P)$ can be denoted by $\frac{m}{n}$, where $m$ and $n$ are both relatively prime, positive integers, compute $10m + n$.