Expanding both sides of the equation, we get:

(x+5)^2 + 1 = (6x-1)^2
x^2 + 10x + 25 + 1 = 36x^2 - 12x + 1

Combining like terms, we have:
x^2 + 10x + 26 = 36x^2 - 12x + 1

Rearranging terms, we get:
35x^2 - 22x - 25 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-(-22) ± √((-22)^2 - 435(-25))) / (2*35)
x = (22 ± √(484 + 3500)) / 70
x = (22 ± √3984) / 70
x = (22 ± 63) / 70

Therefore, the solutions are:
x = (22 + 63) / 70 = 85 / 70 = 1.2143
x = (22 - 63) / 70 = -41 / 70 = -0.5857