Synchronizing MySQL database using master slave approach - Laravel 4

I am using a specific API to fetch data from the server and store it in my DB. Since the size of the data is very large, I do it this way as it takes a long time to fetch in real time. The point is that the main DB can be updated: records are updated, created, or even deleted from the DB. To update the database, one way is to resample the data and check each record if any changes have occurred to it. This method is ineffective.

Is there any other way to keep the DBs in sync between them while ensuring my DB is up to date ?!