I'm installing a dimmer (and thus replacing the left switch in my bathroom) and from the four wall wires only the white and red attach to the left (light) switch and the bare wire (I'm assuming the ground) attaches to the right switch. They seem to operate independently as I can turn on the lights and/or the fan. The dimmer has a green ground wire that they say to attach to the ground however I do not have access to this wire as it is attached to the right switch.
Am I safe installing the dimmer using only the two wires that are attached to the left switch and leaving the ground unattached?