aggregate per variable over which sums are calculated in R data.table

I have some time data

library(data.table); library(lubridate); set.seed(42)
dat <- data.table(time=as.POSIXct("2019-01-01 08:00:00") + round(runif(10,60,1e4)), val=runif(10))[order(time), id:=seq_len(.N)]
> dat[order(id)]
                   time        val id
 1: 2019-01-01 08:12:42 0.93400648  1
 2: 2019-01-01 08:14:33 0.29466004  2
 3: 2019-01-01 08:24:47 0.27195012  3
 4: 2019-01-01 08:43:43 0.52270421  4
 5: 2019-01-01 08:55:16 0.98264672  5
 6: 2019-01-01 09:01:20 0.02388521  6
 7: 2019-01-01 09:39:06 0.89681397  7
 8: 2019-01-01 09:47:16 0.82138170  8
 9: 2019-01-01 10:09:31 0.06342926  9
10: 2019-01-01 10:20:01 0.67328881 10

and I would like to calculate the sum of val during the following hour for each value of time. For example, for ID 1, this would be the sum of val for IDs 1 to 6, for ID 2, the sum of val for IDs 2 to 6, and so forth. In my actual problem, there is an additional grouping variable, which I omitted to keep things focused. I will then implement the solution, adding [..., by=group].

I understand that solving this requires me to subset within j but this is a problem I frequently run into and can't solve. I have not yet understood the general approach to this, if there is one.