Dice and Division

Player $A$ and player $B$ , are playing a game. They each have an unbiased 10-sided dice with faces labelled with the numbers $1,2,3,...,10$ . To play, $A$ and $B$ simultaneously roll their dice. The number that $A$ rolls is denoted as $m$ and the number that $B$ rolls is denoted as $n$ . If $m = n$ then they roll the dice again (ie. it is like the last roll didn't happen). If $|m-n|$ divides $m+n$ then $B$ wins, else $A$ wins. The probability that $B$ wins can be expressed as $\dfrac{p}{q}$ where $p$ and $q$ are coprime positive integers. What is $p+q$ ?