Do I need to change my cassette if I can't see any wear?
That's an impressive amount of mileage on a single chain.  Especially on a narrow 11-speed one.  I'm guessing that you keep everything very well maintained and don't ride in much wet weather?

The two main problems you'll get from a worn cassette are:


Skipping chain (either between cogs or jumping on a single cog)
Premature chain wear (as the chain stretches to match the worn cassette's teeth)


If you're not seeing the first problem and visually the cassette looks fine, then you're probably ok to keep using it.  Best case, everything works fine and you've delayed the cost of using your new cassette.  Worst case, your new chain won't last as long and at that point you'll have to change both.

Since chains cost much less than cassettes, I'd suggest running with the old cassette if it's not skipping and shifts smoothly.