The most common and most likely answer to this crossword clue is the 11 letter word MARSHMALLOW
I've seen this crossword clue in The Times
M
A
R
S
H
M
A
L
L
O
W
More clues leading to the result MARSHMALLOW
Buddy explains!

The straight part
We know that "sweet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sweet = marshmallow.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MARSHMALLOW mean?
MARSHMALLOW noun- A species of mallow, Althaea officinalis, that grows in marshy terrain.
- A type of confectionery, originally (since Ancient Egyptian times) made from this plant, but now generally made of sugar or corn syrup, gelatin that has been pre-softened in water, gum arabic, flavorings, and sometimes beaten egg whites, all whipped to a spongy consistency.
- Someone who is soft and benign.
- To soften (literally or figuratively)