I remember that I've answered a question similar to this previously here. Jumping from 5.1. to 5.5 was really simple to me once.
However, the 5.6 implemented several changes in the database structure and might be harder to accomplish.
I do recommend to make this test on a staging environment and perform several tests before deploying on production.
Just to complement this topic, you may also refer our Switching Database documentation. It describes how to migrate the entire JIRA database to a different DB server.
Hope it helps!
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