First, let's expand the expression using the formula for the square of a binomial:

(6x+1)^2 = (6x+1)(6x+1) = 36x^2 + 12x + 1

Now, we can substitute this back into the original equation:

(36x^2 + 12x + 1)(6x + 1) - 24 = 0

Expanding further:

216x^3 + 36x^2 + 6x + 36x^2 + 12x + 1 - 24 = 0

Combining like terms:

216x^3 + 72x^2 + 18x + 1 - 24 = 0
216x^3 + 72x^2 + 18x - 23 = 0

This is the simplified form of the equation.