smc

Notice that $x_1$ and $x_2$ are the distinct solutions to the quadratic $3x^2-hx-b=0$. By Vieta, the sum of the roots of this quadratic is the negation of the coefficient of the linear term divided by the coefficient of the quadratic term, so in this case $-\frac{-h}{3}=\frac{h}{3},\boxed{\frac{h}{3}}$.