Florescent lights replaced with LED
You have an old-style switch loop

A common wire-saving trick up until very recently was to use a /2 cable to run a switch loop, with one wire for the always-hot and the other for the switched-hot.  This means that a white is used for a hot, though, which is why the NEC specifies that the hot white is supposed to be tagged with a wrap of black (or some other color than white, green, or grey) electrical tape.  However, lazy installers often skipped that because it was "obvious", and the NEC gave them the latitude to do so up until recently.

So, grab some black (or better yet, red) electrical tape and wrap it around the solo white wire -- this connects to the fixture black wire, as it's the switched-hot.  The fixture white wire connects to the bundled white wires, which are the neutral.  Grounds connect together, of course (although you'll have to cut off the crimp used and replace it with a wirenut), and the existing bundle of black wires is not touched (as it's the always-hots -- your existing problem was caused by connecting the fixture black to the bundle of black wires).