Like I suspected, invalid
It would be a valid trade, but you have to add the salary of the pick as well.
14th pick $3,644,040
Nance Jr. $11,709,091
It works with #30 instead of #14 as well.
30th pick $2,040,480
$9,665,037 x 1.25 + $100,000 = $12,181,296.25 > $11,709,091 (Nance's salary), hence it would be a valid trade
Only problem is that drafted rookies may not be traded for 30 days after they sign their contract. Basically we'd have to wait for a month before we finalize the trade. Not a problem whatsoever. For instance, the Cavs did a similar thing in 2014 when they traded Wiggins (#1 that year) + Bennett in a 3-way deal for Kevin Love.