Black Louisianians were voting in the 60's. I was there.
See, Louisiana v. United States, 380 U.S. 145 at 151-52 (1965), in which the court found that interpretation tests, such as Louisiana's requirement that an applicant give a reasonable interpretation of any section of the state or federal constitution, were adopted for the frank purpose of disfranchising Negroes, it being understood that the registration officers would use their discretion for that purpose. And, when the United States attorney general succeeded in having a state literacy statute declared unconstitutional, another slightly different one would be enacted to take its place.