HMMT November 2019 H8

Omkar, $\mathrm{Krit}_{1}, \mathrm{Krit}_{2}$, and $\mathrm{Krit}_{3}$ are sharing $x>0$ pints of soup for dinner. Omkar always takes 1 pint of soup (unless the amount left is less than one pint, in which case he simply takes all the remaining soup). Krit $_{1}$ always takes $\frac{1}{6}$ of what is left, Krit ${ }_{2}$ always takes $\frac{1}{5}$ of what is left, and Krit ${ }_{3}$ always takes $\frac{1}{4}$ of what is left. They take soup in the order of Omkar, $\mathrm{Krit}_{1}, \mathrm{Krit}_{2}$, $\mathrm{Krit}_{3}$, and then cycle through this order until no soup remains. Find all $x$ for which everyone gets the same amount of soup.