jmc

The difference between three-fifths full and one-sixth full is $\frac{3}{5}-\frac{1}{6}=\frac{13}{30}$ of the tank's capacity. Let $x$ be the capacity of the tank in gallons. Since $\frac{13}{30}$ of the tank's capacity is 130 gallons, we have $\frac{13}{30}x=130$. Multiplying both sides by $\frac{30}{13}$ gives $x=300$, so the capacity is $\boxed{300}$ gallons.