Bind input$plotBrush and textInput together - r

Question

I would like to bind input$plotBrush to textInput and vice versa so that when I draw my x brush on my plot it set the same boundaries ([brush]$xmin and [brush]$xmax) to the related text input and when I enter my values in my textInput, it draws me a brush on my plot whith the same boundaries entered.
I wasn't able to find any solution on accessing the [brush]$xmin and [brush]$xmax variable
(problem is : updateBrushInput does'nt exist)
Here is a reproductible example :
(the text inputs are set and returns [brush]$xmin and [brush]$xmax from the brushPlot, but the filter only works in one way)
library(shiny)
library(leaflet)
library(leaflet.extras)
library(tidyverse)
library(sf)
#Create T0New data
lat <- c(49.823, 49.823, 58.478, 57.478, 45.823)
lng <- c(-10.854,-10.854,-10.854,2.021,2.02)
date_start_min <- c(123,125,135,168,149)
T0New <- data.frame(lat,lng)
ui <- fluidPage(
leafletOutput("map", height = "50vh"),
textInput("input1","Date start (from 123 to 149)",value = ""),
textInput("input2","Date end (from 123 to 149)",value = ""),
plotOutput("distribPlot", height = "47vh",
brush = brushOpts(id = "distribPlot_brush", direction = "x", resetOnNew = FALSE))
)
server <- function(input, output, session) {
observeEvent(input$distribPlot_brush, {
brush <- input$distribPlot_brush
if (!is.null(brush)) {
updateTextInput(session, "input1", value=brush$xmin)
updateTextInput(session, "input2", value=brush$xmax)
}
})
#filter data from plot sel
filteredGraphData <- reactive({
currentlyFiltered <- T0New
if(!is.null(input$distribPlot_brush)){
thisSel <- input$distribPlot_brush
currentlyFiltered <- currentlyFiltered %>%
filter(date_start_min >= thisSel$xmin, date_start_min <= thisSel$xmax)
}
return(currentlyFiltered)
})
#Output map
output$map <- renderLeaflet({
leaflet()%>%
addProviderTiles(providers$OpenTopoMap)
})
observe({
mapData <- filteredGraphData()
mapProxy <- leafletProxy("map", session = session, data = mapData)
mapProxy %>%
clearGroup('A') %>%
addCircleMarkers(
data = mapData,
lat = mapData$lat,
lng = mapData$lng,
radius = 5,
color = 'red',
stroke = F,
fillOpacity = 1,
group = 'A'
)
})
#outputPlot
output$distribPlot <- renderPlot({
distribPlot <- ggplot(T0New,aes(date_start_min)) +
geom_density(col = "#053144", fill = "#43a2ca", alpha = 0.3, adjust = 0.75)
return(distribPlot)
})
}
# Create Shiny app ----
shinyApp(ui = ui, server = server)