Calling the ILM Start, Stop, or Put Lifecycle APIs in a mixed 6.5 and 6.6/6.7 cluster will cause the 6.5 nodes to fail to join the cluster with this error:

java.lang.IllegalArgumentException: Unknown NamedWriteable [org.elasticsearch.cluster.metadata.MetaData$Custom][index_lifecycle]

The cause of this is that the ILM custom metadata states that the minimum supported version is 6.5.0 (this constant was never updated when ILM was pushed back to 6.6):

This causes the 6.5 nodes to try to read the custom metadata, but because ILM is not present in 6.5, this fails.

A full cluster restart upgrade to the new version appears to be the only way to resolve the issue if a cluster gets into this state.