Julia 1.0 + Combinatorics, 89 bytes

using Combinatorics
~x=(p=[partitions(x)...])[argmin(keys.((S=p.|>i->sum.(i)).∪0).=>S)]

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Julia 1.7 + Combinatorics, 74 bytes

using Combinatorics
~x=argmin(p->keys(sum.(p)∪0)=>sum.(p),partitions(x))

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argmin(f, itr) needs julia 1.7 or later