NArgMin with Root functions

I’m trying to minimize an error function sumt to find some parameters S, s0, si :

Ris[S_?NumericQ, s0_?NumericQ, si_?NumericQ, so_?NumericQ, R_?NumericQ] =   RR /. Solve[((8 RR*S ((2 RR^2)/R^3 - s0))/R^3 +         8 \[Pi] RR si + (8 \[Pi] RR^2 so)/(R^3 + RR^3)^(        1/3)) == 0, RR][[4]] ri = {54, 55, 62, 66, 62, 66, 71, 75, 77, 79, 94, 89, 99, 113, 124,    123, 140, 157, 163, 176} re = {72, 74, 82, 83, 90, 97, 104, 113, 115, 126, 136, 143, 158, 171,    185, 192, 218, 226, 246, 270} Rdata = (re^3 - ri^3)^(1/3); tableerror =    Table[(Ris[10^S, s0, si, 1, Rdata[[i]]] -        rayoninterne[[i]])^2, {i, 1, Length[rayoninterne]}]; sumt[S_?NumericQ, s0_?NumericQ, si_?NumericQ] =    Total[tableerror]; NArgMin[{sumt[S, s0, si],    8 < S < 11 && 0.001 < s0 < 0.1 && 0.001 < si < 10}, {S, s0, si}] 

But this doesn’t work and I suspect that it is because the Root function in my Ris function. Is it the issue ? And how could I fix this ?