Probability Fundamentals & Geometric Probability · Challenge problem

A subset $S$ of $\{1,2,\dots,10\}$ is chosen uniformly at random among all $2^{10}$ subsets. The probability that the sum of the elements of $S$ is divisible by $3$ (the empty set has sum $0$) is $\dfrac{m}{n}$. Find $m+n$.