Should I give 2 weeks notice at CVS?

I recently got a second job as a partime overnight cashier at cvs. I have another full time job that I work at 6 days a week. My full time job has asked me to come in an hour earlier everyday, which clashes with my time at cvs. I've also been scheduled for 4 days a week instead of the 2 I was told I would when I started. I've been going without sleeping for 2 to 3 days all the time. I've tried to talk to my manager, but she always comes in late or is never in to answer the phone when I call. I've never quit without giving notice before, but I can't find anyone to even notify! I'm not too worried about burning any bridges, because most companies will only give dates of employment/position because they're afraid to get sued for defamation (I just read an interesting article on that). Should I give notice?
Should I give 2 weeks notice at CVS?
Post Opinion