Most dump valves use a knot on the other side of the poppet to hold the cord in place. You need to dissassemble the valve and then gently peel off the rubber disc on the other side to expose the cavity where the knot lies. Then re-insert and re-knot the cord and replace the rubber disc (it should still stick, it not use a bit of rubber cement) and reassemble the valve.
I am not sure about dive rite valves in particular, but I would be surprised if they were different.
I would not use epoxy as murphy's law dictates it will fail ecaxtly when you need to dump air to avoid blowing a deco stop, safety stop, etc.