Cool Hand Luke - why no black convicts?

Just watched Cool Hand Luke again. Great movie but I noticed for the first time that there was not a single black actor in it. (When I first saw it in 1967/8 I didn’t think about that at all, I guess audiences had different expectations then.)

So was the movie reflecting the reality of Southern prison farms back then (the 60s), were they completely racially segregated?

Many prisons were segregated through the 1960s.

In fact, one unintended consequence of desegregation was the rise in prison gangs. As different racial and ethnic populations were merged together there was a pretty significant impact on internal social politics and what group would control what aspects of prison life.