On |z|=1, constant 11 dominates |z⁶+5z³+4z|≤10, so Rouché gives zero roots inside. On |z|=3, |z⁶|=729 dominates |5z³+4z+11|≤135+12+11=158, so all six roots lie inside. Strict inequalities exclude boundary zeros. Annular count = **6**.
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