What is your routing setup on the LTM?
For example, we have an LTM that has a single global default route (any any forwarding IP VS) with a single trunk to a 6k switch. With this method, you SHOULD NOT establish another trunk with another NXOS switch. It is of course possible but you will have a lot of problems that have been stated above.
We do have an LTM that have multiple "transits" (multiple forwarding IP VS) that go to our 6k, our NXOS, and our ASA to follow our PCI compliance rules. This is best maintained if you utilize the vlan access lists on the VS configs.
Either way, you will need to make sure that routing and STP is properly configured across all devices for fail over. I personally have mac masquerading setup on the LTMs to keep this second example working, in case of a failover, but I have "heard" (rumored) that it is not needed anymore but Im more of a "Ill believe it when I see it" kinda guy!
HTH
-e