I connected my Dell Inspiron with Ubuntu 16.04 installation to an external monitor earlier, I had headphones plugged in and the sound was working fine at this point.
I earlier removed the HDMI cable from the laptop and since then I have had no working sound through either the laptop or the headphones connected.
Through PulseAudio Volume Control, under Configuration, I see only HDMI output profiles, and no default built-in audio profile.
I see no output devices listed under 'Play Sound Through' on the Sound Settings interface.
Plugging the HDMI port back into the laptop gives me an option for HDMI / DisplayPort on the Sound Settings interface