UTG KK flopped Top Set => river completes flush...

The point is now you are missed a lot of value when he floped sets or 2 pairs. Or he lost minimum by having a huge draw. He can also x/raise as a bluff on the river and then you have to fold.
To prevent all this bet higher flop reraise his raise. Bet or raise turn for value. River is tricky, so when you build the pot till river you can check behind now.

simply push river. Even if villain bluff raises some of flush draws on flop, he would mostly bet flushes on river so you can put him mostly on total air that folds anyway or some sets, 2 pair. Flop i would 3bet due to being draw heavy board.

Thank you pokerboy198229 and mlatasrb for leaving a comment.

I found you very passive on the flop and on the turn, having to play those big hands aggressively so it would raise right on the flop (charging 2pairs, FD, sets and etc). Fast play your big hands

Yes, Andrepipocado i guess you are right playing a bit more agressivly should be better...

i did it in this hand....

Poker Stars, $0.05/$0.10 No Limit Hold'em Cash, 6 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

SB: $10.13 (101.3 bb)
BB: $11.41 (114.1 bb)
Hero (UTG): $11.14 (111.4 bb)
MP: $10.71 (107.1 bb)
CO: $12.39 (123.9 bb)
BTN: $7.70 (77 bb)

Preflop: Hero is UTG with 6♥: 6♦:
Hero raises to $0.30, MP folds, CO calls $0.30, BTN calls $0.30, 2 folds

Flop: ($1.05) 5♠: 7♠: 6♣: (3 players)
Hero bets $0.50, CO raises to $1.80, BTN raises to $4.30, Hero raises to $10.84 and is all-in, CO raises to $12.09, BTN calls $3.10

Turn: ($30.13) Q♣: (3 players, 1 is all-in)
River: ($30.13) A♥: (3 players, 1 is all-in)

nice man
GL!

66 set hand is almost overplay to 3bet unless he is super agro with bluff raises or merges top pairs. board is connected offering many straights so it differs from your KK hand a lot.

First hand is stack-off on flop, no need to slow play.
Second hand if different, middle set conected bord, no nuts on flop...