We know that slaves were covered because the 14th says, "All persons born or naturalized in the United States, and subject to the jurisdiction thereof," which qualification was met by former slaves.* We also know from history (some of us do) that the 14th was one of the three post-Civil War amendments intended to address the end of slavery, the rights of former slaves, and other consequences to the states and citizens of states who were "in rebellion."
Where did you get this idea that when understanding the Constitution, one must take an 'Exact words, Gregg!" approach?
*To save you the typing, of course we are talking about slaves in the American states which allowed slavery. No it did not include slaves in other nations, or slaves in Greek history, etc. Going by exact words, it should not have included any slaves still living who were imported rather than born in the United States. Nor any children of Thomas Jefferson's slaves if they were born while TJ was visiting France with his human "property."
I'm guessing that no one made that distinction and all slaves were granted citizenship, as the amendment's framers intended.