Yes, this is possible. I did this successfully in a production environment this week.

A full dataminer + DB backup was taken from a v3.7 setup and this was restored on a clean agent, running Cassandra v3.11.8.

1 issue occurred
C:/Program Files/Cassandra/logs/system.log -> "Cannot start node if snitch's data center (dc1) differs from previous data center (datacenter1)"
SOLUTION: stop cassandra and remove or rename the local folder:
C:\ProgramData\Cassandra\system\local-7ad54392bcdd35a684174e047860b377

That's the table where the datacenter reference is stored, this will automatically be created again during next Cassandra startup.

1 recommendation
after the backup restore, open nodetool
Open cmd in location C:/Program Files/Cassandra/bin

Run "nodetool upgradesstables"

This will create the ss tables again based on the new version to minimize any compatibility issues.

Note 1
You'll need to check a couple of things prior to the restore. In C:/Program Files/Cassandra/conf/cassandra.yaml:

• ClusterName
• Seeds
• DiskOptimizationStrategy
• DataPath

Note 2
On the clean agent, it originally had v3.7. Meaning that I first had to uninstall Cassandra (DM Help - there's a step on Cassandra).
Followed by the standalone Cassandra installation (DM Community).
For me it was easy since it was only a single agent/node, I could use the localhost_configuration.xml (change what's needed inside + see note 1)

Note 3
This was not tested on failovers or cluster.