I think the solution in the video you linked to is incorrect. There should be a third imaging considered, because the light physically returns through the lens. The person in the video is treating the system as if it were two lenses, but mirrors and lenses are different in that light can go through a lens both ways, while it cannot go through a mirror. Hence, mirrors cannot have "virtual objects" in the way that lenses do, because a "virtual object " supposes the possibility that a real object could be there -- which, for a mirror, is impossible.
I would say that, in the problem, you would need to consider the image made by the lens being positioned to the left of the mirror (instead of "behind" the mirror), and then treat that as the virtual object for the lens again, and find the image of *that*. I will think about it more, but I am pretty sure that would be correct.