Adding non-iTunes music to iOS 8.4

If you've updated to iOS 8.4 and find that music from your library that was not purchased from the iTunes Store is no longer on your device, you may discover that you cannot add that music from iTunes back to your iOS device. When you try to delete music that's on the device using iTunes, nothing happens. When you try to add music from iTunes, you may get a message that you cannot because iTunes Match is enabled (even if it isn't).

What I found is that if you go to Settings > Music > iCloud Music Library OFF on your iOS device, you should again be able to manage your music in iTunes.