What did you use to actually cure it?

Meds.

Is this the kind of depression that was probably a result of a random imbalance of neurotransmitters, rather than anything actually going hugely wrong in your life?

That distinction is pretty artificial. If you must know the history, my childhood sucked big time in several different ways. When circumstances improved, the depression made my life get worse rather than better. Then I got on meds, so the depression went away and I could start picking up the pieces.

be newly and frighteningly negative

Sure, if you're in okay circumstances and it doesn't creep up on you and you can do something about it. If you don't actually remember the last time you were healthy, it just feels normal.

If there are hugely wrong things with your life but you're just too lazy and scatterbrained to fix them, it's a great idea to put them on the back burner and go fix your brain first.