SELECT 
  * 
FROM 
  cscart_mb_salvage_cases 
WHERE 
  auction_product_id IN (
    10766, 10767, 10768, 10776, 10781, 10789, 
    10791, 10792, 10793, 10796, 10797, 
    10801, 10806, 10807, 10812, 10815
  ) 
  OR sale_product_id IN (
    10766, 10767, 10768, 10776, 10781, 10789, 
    10791, 10792, 10793, 10796, 10797, 
    10801, 10806, 10807, 10812, 10815
  ) 
ORDER BY 
  updated_at DESC, 
  case_id DESC

Query time 0.00032

JSON explain

{
  "query_block": {
    "select_id": 1,
    "read_sorted_file": {
      "filesort": {
        "sort_key": "cscart_mb_salvage_cases.updated_at desc, cscart_mb_salvage_cases.case_id desc",
        "table": {
          "table_name": "cscart_mb_salvage_cases",
          "access_type": "ALL",
          "rows": 58,
          "filtered": 100,
          "attached_condition": "cscart_mb_salvage_cases.auction_product_id in (10766,10767,10768,10776,10781,10789,10791,10792,10793,10796,10797,10801,10806,10807,10812,10815) or cscart_mb_salvage_cases.sale_product_id in (10766,10767,10768,10776,10781,10789,10791,10792,10793,10796,10797,10801,10806,10807,10812,10815)"
        }
      }
    }
  }
}