I tried to add my cell phone number into the directory (since my home phone number doesn't work anymore) but I did not see any "edit" button in my profile. It's just not there. Does anybody know why that is?
You should see a "Edit" button top center when you pull up your information. However, I think that only works for the Head of House and spouse. It may not work for children, even if they are adults.
Have you searched the Help Center? Try doing a Google search and adding "site:churchofjesuschrist.org/help" to the search criteria.
So we can better help you, please edit your Profile to include your general location.