LLMs cite. So hope they did their due diligence.
You can only correct for missing entries by doing the same work you’d need to start from scratch. But after that you now have a second list to consider.
Of course it’s not the kind of question you can get an objectively correct answer for, but you could come up with the correct answer for a given methodology.
Especially in cases such as this. For well known works of literature and music structured data exists already.