I have the same situation in my application.
When the user clicks the edit button, I show an extra table cell at the end of my table, which allows them to add a new record. Not sure if this is possible in your case.
Maybe add it at the beginning or insert a button just above the UITableView? Then you can also outline the “Add / Change” button so that it is clear that this is how they can add new entries, although I did not.
Another option would be that this extra button or table cell is always visible.
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