I'm not with Laminar Research, just a fellow simmer in the UK.
According to J.Roberts of LR in 2017, the inbuilt default video recorder in X-Plane 11 is not currently able to record audio, something that I would confirm from my own experiences of such.
You will therefore need to download third party software capable of recording video and audio.
In that regard, you may be interested in an article on the Techradar website which reviews a number of 'free' screen recorders, please see https://www.techradar.com/news/the-best-free-screen-recorder
From the software covered in the article, I have already downloaded what Techradar consider to be the best and that is the one from OBS Studio. The software takes a short while to get used to, but it appears to work very well whilst recording from any number of sources, including X-Plane 11 (with full sound!)
The software can be downloaded from https://obsproject.com/download
and there is a good amount of helpful information about it here https://obsproject.com/wiki/OBS-Studio-Overview#scenes-and-sources
Have a look through and try it, it may be just what you're looking for?