Maybe so:
func = Sum[Abs[x - (3*k - 55)], {k, 1, 28}]; sol = Minimize[func, x] Plot[Labeled[func, {"minimum"}, {Below}], {x, -20, 0}, PlotRange -> {Automatic, {580, 630}}, Epilog -> {Black, PointSize[0.02], Point[{x /. sol[[2, 1]], sol[[1]]}]}]
