I have a Dell Inspiron 3181 Chromebook.
I have removed ChromeOS and replaced it with the most recent version of Linux Mint using the following tutorial: https://www.youtube.com/watch?v=AxsckwmRhfw
I have tried almost every tutorial out there to fix my lack of audio, for every distro used thusfar. Prior to Linux Mint, I tried installing Ubuntu, Lubuntu, Xubuntu, Fedora, etc. to see if the compatibiliy error was distro-related. No effect.
Documentation from this tutorial's creator in regards to compatibility is here (it is archived and no longer maintained - did not see any glaring issues): https://johnlewis.ie/custom-Chromebook-firmware/rom-download/
My hardware specifications are located in Dell's User Manual here (audio hardware information is located on pages 16 and 17): https://topics-cdn.dell.com/pdf/inspiron-chromebook-11-3181-2-in-1_users-guide_en-us.pdf
If you comment a solution, I will reply with whether not I have tried it instead of listing all of the ones I've attempted.
If you need more information, I will track this post vehemently and respond with the information you need.