Linksys modems tend to act as a nat. You may need to forward a port thru it depending on the model. Can you have a close look at it & find out what the model no. is & post it back please. There should be a model number on the top, side or bottom.
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the modem connects to a router
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So you have a separate router. What brand & model is your router? This might also require port forwarding.