MathNet 2020 — Math Olympiad Vault — Part 05 Question 76

In the figure, triangle $A B C$ is equilateral and $B D = C E = A F = \frac{A B}{3}$. The ratio $\frac{E G}{G D}$ can be written as $\frac{m}{n}$, $\gcd(m, n) = 1$. What is $m+n$ ?