x can be any real number
As long as it is to the power of 0, it will equal one. And because 6^0 = 1, 1^x can be any positive number, and it will still give you one.
As stated by WojtekR, even negative numbers can get 1
x = - 5
(6^0)^-5 = 1^-5 = 1/1 = 1
~ Thanks @WojtekR