I've been looking into this. The manual for the 685 shows a power port, the 350 doesn't have one. Godox makes a battery pack, see here, but they don't specify a cable for it. They do show the 685 with a battery pack connected somewhere so there must be a cable. I've read that B&H knows which cable so you can ask them. Unfortunately, the Godox website shows the power pack but has no info on which cable fits it.