Find the region after using Minimize?

[dirac (dirac fang)]

i use below command calculator mininum

Minimize[Sum[Abs[x - (3*k - 55)], {k, 1, 28}], x]

the answer is {588, {x → -13}}
mininum is right but x must be a region.how can i find the right region.
thank

[mariuszi28cg (Mariusz Iwaniuk)]

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]]}]}]