Solve the equation involving absolute value. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
$$|3-4x|-1=5$$

Step 1 ：The absolute value equation can be solved by considering two cases: when the expression inside the absolute value is positive and when it is negative.

Step 2 ：In the first case, we have $3-4x-1=5$, and in the second case, we have $-(3-4x)-1=5$.

Step 3 ：We can solve these two equations separately to find the possible values of $x$.

Step 4 ：For the first equation, we get the solution $-\frac{3}{4}$.

Step 5 ：For the second equation, we get the solution $\frac{9}{4}$.

Step 6 ：We have two potential solutions for the equation, -3/4 and 9/4. However, we need to check if these solutions are valid by substituting them back into the original equation.

Step 7 ：Both solutions, -3/4 and 9/4, are valid.

Step 8 ：Therefore, the solutions to the equation are $\boxed{{\displaystyle -\frac{3}{4},\frac{9}{4}}}$.