The label won't say; you'll have to look for the cable (currently not in use, but present, perhaps tied out of the way).
In any case, I don't see anything online about your specific PSU, but some general things about WinPower that make me doubt its quality. If it does not have a PCIe power cable, I would NOT use an adapter, as it may not have the actual +12V amperage to power a video card (regardless of what's on the label).
A 380W Antec Earthwatts or 360W Seasonic G360 would have no trouble powering a HD6770 or even a HD7850.
If replacing your PSU is not an option, look for a HD7750 instead. Almost as powerful as the HD6770, it needs no auxiliary power cable.