i know this might be simple, but i am so confused about what to
solve using any method.

So just cube both sides: (³√1-2x)³=3³
The cube root and the cube exponent cancel each other out, so then you just have to cube the 3: 1-2x=27
Now solve like normal:
1-2x=27
1-2x-1=27-1
-2x=26
-2x/-2=26/-2
x=-13

Now check! :
(³√1-2(-13))=3
(³√1+26)=3
³√27=3
3=3 √

:) I hope that helps and makes sense :)