It is easiest to sell cheap sewing cabinets online using specialized buy-and-sell sites such as eBay or Craigslist. These are user-to-user transaction sites and don't require any kind of intermediary.
Other places to try to sell cheap sewing cabinets are local secondhand furniture consignment shops. Utilizing a consignment shop allows the seller the freedom to barter a price, just like selling online, but guarantees cash in hand at the end of the transaction.
Selling online is simple and easy with good pictures and accurate information. There is likely to be a waiting period between listing and buying. Interested parties may not always come through on a final transaction, however.
If selling proves to be a challenge, it is always possible to donate a sewing cabinet to a local thrift store.