# Different method for the same question = different post?

In the post Finding all solutions to $y^3 = x^2 + x + 1$ with $x,y$ integers larger than $1$, the OP presents a certain method of solution, and asks for advice.

While perusing it, I had a brainstorm for a very different method of attack. But I'm stuck half-way through my own solution, and want to get some help. Should I start a new, linked post (to acknowledge the different method being used), or post an answer or comment in the existing thread (to acknowledge that I'm trying to solve the same equation)?