What is the cheapest way of backing up my 11TB of data on my NAS?
Asustor Nimbustor AS5304T (3x10TB RAID 5)
There are three options there. Backing up to the cloud, USB drive or cheap secondary NAS.
Cloud storage will cost $660/year
Comparison with other service providers: https://www.backblaze.com/best-online-backup-service.html#af9rgr
Or set up automated backups to your basement or friends house using a cheap Synolo9gy NAS. (If your friend has a NAS already you can back up to each other NAS).
shucking an external hard drive is a popular option.