An 8-pin PCIE connector per the spec should be able to supply 150W of power through the cable (although, most PSU manufacturers rate their cables for higher than that... I wouldn't necessary risk it in this environment). The slot can only provide up to 75W.
The 6700XT can draw 220W under typical gaming loads... not considering any overclock. You're cutting it way too close by trying to power that card with a single PCIE power cable.
550W might be enough depending on what the rest of your system is, but the single PCIE cable is a worry. I would recommend getting a 650W as recommended by AMD, and confirm that your new PSU has the necessary cables to feed the GPU.