1. The problem asks if the equation $6x - 11 = -72$ correctly represents "Six times the difference of 11 and a number is -72."\n\n2. Recall the phrase "difference of 11 and a number" means $11 - x$, not $x - 11$.\n\n3. The expression $6x - 11$ means "six times the number, then subtract 11," which is different from "six times the difference."\n\n4. The correct equation is $6(11 - x) = -72$, not $6x - 11 = -72$.\n\n5. To verify, solve $6x - 11 = -72$:\n$$6x - 11 = -72$$\nAdd 11 to both sides:\n$$6x - \cancel{11} + \cancel{11} = -72 + 11$$\n$$6x = -61$$\nDivide both sides by 6:\n$$\frac{6x}{\cancel{6}} = \frac{-61}{\cancel{6}}$$\n$$x = -\frac{61}{6}$$\n\n6. Now solve the correct equation $6(11 - x) = -72$:\n$$6(11 - x) = -72$$\nDivide both sides by 6:\n$$\frac{6(11 - x)}{\cancel{6}} = \frac{-72}{\cancel{6}}$$\n$$11 - x = -12$$\nSubtract 11 from both sides:\n$$11 - x - 11 = -12 - 11$$\n$$-x = -23$$\nMultiply both sides by -1:\n$$x = 23$$\n\n7. Since the solutions differ, $6x - 11 = -72$ is not the correct equation for the problem.\n\nFinal answer: No, the equation $6x - 11 = -72$ is not correct for the given problem.