The HD7560D is not an additional card, it's the igpu built into your APU (that's an AMD cpu + graphics), so as such, that 700w excuse for a psu has had nothing heavier on a draw than the fans, your drives and the APU, all of which adds upto between 150w-200w at best.
Even that fire-starter wouldn't have an issue with such a low wattage.
The issue comes with you adding another actual component, the 750ti pulls @ 70-75w, the 760 pulls @ 170w.
With your psu at 30A on the 12v rail, that's a total of @ 360w. Your pc already pulls @ 200w (worst case), so adding a 760 puts you over the limit, even the 750ti will push the system to 250w+ on a very unreliable 360w.
You are stretching that rubber band very tight, which usually is ok, but not advisable, but in your case it's also a 5 year old rubber band, and then that becomes a question of not 'if' it will snap, but 'when' and how much will it sting when it does.
To put it into perspective, that psu has a 1 year manufacturers warranty, when everyone else decent has a minimum of 5 years, some upto 12 years. That's how much faith they have in what they make.