How to upgrade iDRAC firmware and BIOS of Dell PowerEdge R510?

As shown in the training video in section 4 of the support article Dell PowerEdge: How to a Remote Firmware Update with the iDRAC?, you must manually unzip iDRAC6_1.85_A00_FW_IMG.exe and upload the actual image file firmimg.d6 to the iDRAC. The more recent iDRAC models can accept the executable file directly and unzip it themselves, but apparently the iDRAC 6 can't.