To solve this issue it is really bothering me. The fixes that I saw and tried (there are many-...-many) are all just attempts, "hacks", no simple or bullet proof solution. It was like a miracle that somehow my speakers started to work, now I would need another to get the headphone working. There is a similar question with Dell XPS 13, neither did that solution work for me (I already have the dialog to choose between headset and headphone after I plug in my headset but no sound is coming out on it). Tried alsamixer to unmute, turn on volume on headphones/headset, no luck.
For related system info see the launchpad question/bug that I have reported but seems to be quite there, didn't receive any response yet.
So this is all you can get with a Dell business class laptop that is certified for Ubuntu by Canonical?... Sad to say but I got disappointed in Ubuntu, Canonical. These problems with headphones are not dealt with priority, this was a problem 10 years ago and it is still. I need the headphones to watch courses/tutorials necessary for work... if I don't get a solution in a few weeks I will have to switch to Windows.