A combinatorial interpretation for $n$-ary trees for negative $n$

Question

The ordinary generating function $T_n=T_n(x)$ for the $n$-ary trees satisfies the functional equation $$T_n=1+xT_n^n.$$ This usually applies for $n\ge 0$, but the functional equation can be extended to negative $n$. Writing $$T_{-n}=1+xT_{-n}^{-n},$$ we obtain, by dividing through by $T_{-n}$, that $$T_{-n}^{-1}=1-x(T_{-n}^{-1})^{n+1},$$ i.e. $$T_{-n}(x)=\frac{1}{T_{n+1}(-x)}.$$ What would be a natural way to interpret this combinatorially? I.e. what are "$n$-ary trees" for negative $n$, why do we get the extra 1 degree, etc.