Even if you have a cat 6 rated cable depending on the cable itself, the NIC and your router will validate if it can reach 1GB speeds, if the twisted pairs in the cat 6 cable are degraded in anyway then the NIC and the router will negotiate to a speed it can support, which may be your issue here. I would try using another cat 6 cable you know is good to validate if its just a bad cable or not.
Even if you have a cat 6 rated cable depending on the cable itself, the NIC and your router will validate if it can reach 1GB speeds, if the twisted pairs in the cat 6 cable are degraded in anyway then the NIC and the router will negotiate to a speed it can support, which may be your issue here. I would try using another cat 6 cable you know is good to validate if its just a bad cable or not.
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or lets say ha