Find all real $x$ such that $(2^x-4)^3+(4^x-2)^3=(4^x+2^x-6)^3.$

Enter all the solutions, separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find all real $x$ such that $(2^x-4)^3+(4^x-2)^3=(4^x+2^x-6)^3.$

Enter all the solutions, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{2}, 1, 2
Find all real $x$ such that $(2^x-4)^3+(4^x-2)^3=(4^x+2^x-6)^3.$

Enter all the solutions, separated by commas.
train