jmc

Rearranging the equation gives $6t^2-41t+30=0$. Factoring gives $(t-6)(6t-5)=0$, so the solutions to the equation are $t=6$ and $t=\frac{5}{6}$. The positive difference between these solutions is $6-\frac{5}{6}=\boxed{\frac{31}{6}}.$