xSQL Software has developed a set of tools for this type of database operation. You can use xSQL Data Compare . To achieve the result, you need to specify the left and right database, perform a comparison, and then to add the data that is missing to the left of db to the right db, you need to remove the synchronization for the correct rows and generate and execute the script command.
Here you can see that the lines are not marked: 
And, as you can see, the script does not generate any DELETE statements, only INSERTS for rows that are not in the right DB

Hope this helps!
Disclosure: I am associated with xSQL software
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