A dartboard is the region $B$ in the coordinate plane consisting of points $(x,y)$ such that $|x|+|y|\le 10$. A target $T$ is the region where $(x^2+y^2-40{)}^2\le 100$. A dart is thrown and lands at a random point in $B$. The probability that the dart lands in $T$ can be expressed as $\frac{m}{n}\cdot \pi$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?