If the string is at least consistently built in the format you gave, you could use this:
NSUInteger rangeStart = [string rangeOfString:@"result:"].location;
NSUInteger lastBrace = [string rangeOfString:@"}" options:NSBackwardsSearch].location;
NSUInteger jsonStart = rangeStart + [@"result:" length];
NSUInteger jsonLength = lastBrace - jsonStart + 1;
NSRange jsonRange = NSMakeRange(jsonStart, jsonLength);
NSString *justJson = [string substringWithRange:jsonRange];
Here's a slightly more concise, but perhaps less efficient, method:
NSUInteger rangeStart = [string rangeOfString:@"result:"].location;
NSString *justJson = [string substringFromIndex:rangeStart + [@"range:" length]];
NSUInteger lastBrace = [justJson rangeOfString:@"}" options:NSBackwardsSearch].location;
justJson = [justJson substringToIndex:lastBrace+1];