To solve this equation, we first need to simplify both sides by using the rules of exponents.

On the left side:
36^x (1/6)^(2x-1) = (6^2)^x (1/6)^(2x-1)
= 6^2x 6^-(2x-1)
= 6^2x 6^-2x * 6
= 6

On the right side:
216^x+1 = (6^3)^(x+1)
= 6^(3x+3)

So, the equation simplifies to:
6 = 6^(3x+3)

Since the base on both sides is 6, we can equate the exponents:
3x + 3 = 1

Now, solve for x:
3x = -2
x = -2/3

Therefore, the solution to the equation is x = -2/3.