Dumping is done by putting the presets in the internal banks first and then copying them wholesale to the cartridge.
Do look out for the cartridge size - those of the DX7 mk1 are less wide (about 6mm / a quarter inch) than those of the DX7s, DX7II and DX7IIFD.
I've got a RAM cart for both my DX7 and my DX7IIFD - while it's handy to augment the anemic memory, if you have yours hooked up in the studio to a computer it's not that important.
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Also, another question, is there some way to restore the factory settings on the internal memory on the DX7?
☮ Dave Benson's DX7 Page ☮ has the factory patches (scroll down or search for "factory").