Adjusted for inflation, $15 is still an all-time high. Meanwhile, we're importing millions of unskilled workers from abroad, so there is effectively an infinite supply, or at least a supply that dwarfs demand. A $15 national minimum wage is truly a prescription for disaster. (As we will see demonstrated in the locales that are instituting it. There were far fewer technological options available to replace low skilled labor in 1965.)
From the chart you posted the minimum wage reached it’s peak in 1968 at an inflation adjusted $10.56 per hour in 2012 dollars or $1.60 per hour in 1968 dollars. You need to reevaluate your conclusion.