Totally feasible ... and I have seen it done with over 100m of cable from faceplate to modem. Fortunately not much noise and it worked.
However, in your case: The comms room with be electrically noisy, running through the cable bundles will expose it to further noise from other signals and you will almost certainly loose potential for higher data rates. You need to keep the noise pickup to a minimum.
Put the modem in the comms room and then the output from that can go through the internal Cat5 cabled network to your router.
And there is no need for RJ11/RJ45 adapters - an RJ11 will plug into an RJ45 socket although if you do as I suggest you will not need them.
M H C
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