The problem with Smith & Wesson is that the company would serial nmber frames before they were assembed into guns. Then they woulde draw on their inventory of frames to sometimes make several different models. As a consequence all one can do is say that a particular frame could have been made during a time period of a year - or several years.
If you want to know the exact details you can write the company. Along with the letter which fully describes the gun, including the serial number, you need to enclose a snapshot of the gun and a check made out to S&W in the amount of $30.00 For this modest fee (some others charge three times as much or more) Roy Jinks, S&W's historian will research the records and send you a formal letter containg all of the information reflected in those records.
The best that I can say is that serial numbers K715997 through K779162 were made during 1967. However your revolver could have been assembled during that year, or any year thereafter. That said, it is most likely it was made in 1967.