Syncing computer music with apple music

I currently have Apple Music synced between my iPad and iPhone. I have some music downloaded on my computer that isn't available in iTunes. I checked the music I wanted to sync on iTunes, checked the box that says "sync only checked songs and videos" and hit sync on the bottom. Nothing synced onto my iPad. Tried multiple times, nothing happened. A coworker played around and received a notification saying something along the line of I have iCloud Music Library enabled so it cannot sync. If I turn that off all of my Apple Music on both devices gets deleted. I HAVE to have the specific music off of my computer for work and would love to not lose all of the Apple Music I have. Surely there is a way to work around it.

iTunes and my iPad are up to date.