Peter Town, Yes it does appear the headphone jack is soldered to the board and further damage could result from inexperienced person trying to resolder or replace because of heat required to resolder/replace. Below are a couple links, partial disassembly guide to get you inside to check out the jack. 3rd link shows how a jack is replaced so you can see what may be involved, in case you would like to try it. If not wanting to attempt the repair your self pop into a local good computer repair shop for an estimate. Good luck. I hope this helped you out, if so let me know by pressing the helpful button.
Dell Chromebook 11 CB1C13 Battery Replacement
http://dev.chromium.org/chromium-os/deve...
https://www.youtube.com/watch?v=EICrlw3G...