It's actually before you get to that first chamber (the one with the dead trolls and the first crystal you break) - apologies, I had tried to upload a screenshot but the file size was too big, hadn't realized it failed to upload there.
The exit door is before that point - so enter the cave itself, and you should see the path branch to the right shortly after you enter.
Hopefully this file works... And here is another angle, with the cave entrance circled, and the path to follow here (so as you enter the cave, this would be on your right).