Mac mini hard drive recovery w/ encrypted partition
You have two problems: FileVault whole disk encryption and the HFS+ filesystem. HFS+ is not difficult to deal with in Ubuntu, but I've seen no readily accessible tools to access a FileVault encrypted volume even when you know the password.

It'll be far easier to use a Mac to turn off FileVault. Disk Utility can unlock and decrypt the drive. The folks at the Apple Store might let you use one of the computers in the store to decrypt the drive, otherwise you might have to borrow a friends Mac for a while. It'd be best to use the same version of OS X or newer.