The story
While Mikhail Bakunin is credited with coining this term, it is in fact found in Sam Dolgoff's loose translation [1971] of a fragment [c. 1872], which Bakunin wrote in French and contains no word translatable literally as aristocracy of labo(u)r. In an unsent letter to the journal La Liberté in Brussels [5 October 1972], Bakunin used the wording: “a new aristocracy, that of the urban and industrial workers”. For further etymology, see labo(u)r aristocracy.
Etymology from Wiktionary, CC BY-SA 4.0.